Comparison of three empirical force fields for phonon calculations in CdSe quantum dots

Abstract

Three empirical interatomic force fields are parametrized using structural, elastic, and phonon dispersion data for bulk CdSe and their predictions are then compared for the structures and phonons of CdSe quantum dots having average diameters of ~2.8 and ~5.2 nm (~410 and ~2630 atoms, respectively). The three force fields include one that contains only twobody interactions (Lennard-Jones plus Coulomb), a Tersoff-type force field that contains both two-body and three-body interactions but no Coulombic terms, and a Stillinger-Weber type force field that contains Coulombic interactions plus two-body and three-body terms. While all three force fields predict nearly identical peak frequencies for the strongly Raman-active "longitudinal optical" (LO) phonon in the quantum dots, the predictions for the width of the Raman peak, the peak frequency and width of the infrared absorption peak, and the degree of disorder in the structure are very different. The three force fields also give very different predictions for the variation in phonon frequency with radial position (core versus surface).The Stillinger-Weber plus Coulomb type force field gives the best overall agreement with available experimental data.3

Exciton-optical phonon coupling in II-VI semiconductor nanocrystals

“…Our group has investigated this using empirical force fields for CdSe quantum dots and has found that different force fields predict significantly different extents of disorder in the crystal structure and extents of localization of the phonons. 37 Thus, while we may have a very good description of the longitudinal optical phonon at the unit cell level, we lack a clear picture of what the various LO phonons look like across the whole nanocrystal.…”

“…While density functional theory calculations of EPC have been reported for some structures of the size commonly studied in experiments, 35 usually the ground-state equilibrium geometry and force constants needed to determine the phonon modes are obtained by using empirical force fields parameterized through comparison with experiment and, in some cases, electronic structure theory. [37][38] The excitonic wavefunctions are modeled as the electron and hole functions calculated from an effective mass approximation using a confining potential of appropriate size and shape, with varying degrees of sophistication. 36 EPC in semiconductor nanocrystals is usually partitioned into two contributions, the deformation potential coupling and the Fröhlich coupling.…”

Resonance Raman Spectroscopy and Electron–Phonon Coupling in Zinc Selenide Quantum Dots

“…CdSe and ZnSe quantum dots of the sizes typically studied experimentally have several hundred to many thousands of atoms and are too large to be handled routinely with high-level atomistic electronic structure methods such as density functional theory, although such methods are widely applied to smaller clusters. Rather, calculations on quantum dots of this size are often carried out by using an empirical force field to calculate the ground-state geometry and phonon modes, 1 and a particle in a sphere effective mass approximation (EMA) model to calculate the excitonic energies and wavefunctions. [2][3][4] We have employed these models in previous studies 4 aimed at understanding the electron-phonon coupling in CdSe quantum dots and how it depends on size and/or the presence of a CdS shell.…”

Simulations of nonradiative processes in semiconductor nanocrystals

“…The atomic positions are then relaxed using molecular dynamics-based geometry optimization with previouslyparameterized force fields, 79,105 which includes two-and three-body terms to enforce tetrahedral bonding geometries, to produce NC configurations that are relatively crystalline in agreement with experiment. 106 In the case of core-shell structures, the core is cut from bulk, and the shell material is grown on the surface using the lattice constant of the core material. The subsequent geometry optimization allows the shell to relax and results in compressive strain on the core to minimize the stress along the core-shell interface.…”